I think it's a similar reason to the west's low birth rate : women have more choice and therefore, a larger portion is choosing to have kids later in life (or are finding it more difficult to get a partner, as they require one that surpasses themselves in earning/status etc).

I think you will find that rural areas of china has a higher birth rate than urban areas, as the opportunities in rural areas are fewer. But as more and more people move to urban areas for economic prosperity, the same birthrate will befall them just like in western advanced economies.